Details

analyze731.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample216.0ms (2.3%)

Algorithm

1×

intervals

Results

33.0ms	53×	body	1024	valid
29.0ms	68×	body	1024	invalid
15.0ms	135×	body	128	valid
11.0ms	37×	body	512	valid
8.0ms	33×	body	512	invalid
8.0ms	95×	body	128	invalid
4.0ms	25×	body	256	valid
4.0ms	6×	body	2048	valid
2.0ms	11×	body	256	invalid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

19.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.7b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	5.4b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series49.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

37.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
3.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify202.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
281×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

172 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3960
1	572	3266
2	2075	3044
3	4373	3044
4	4843	3044
5	4992	3044
6	4994	3044
7	4848	3044

prune123.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	2	170

Error

0.0b

Counts

170 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4485 to 1659 computations (63% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.0b	(sinh.f64 l)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series110.0ms (1.2%)

Counts

3 → 84

Calls

3 calls:

71.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
31.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(sinh.f64 l)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
581×	`fma-neg_binary64`
432×	`*-commutative_binary64`
278×	`associate-+l+_binary64`
224×	`associate--l+_binary64`

Counts

125 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2596
1	465	2480
2	1467	2171
3	4147	2171
4	4936	2171
5	4957	2171

prune80.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Error

0.0b

Counts

91 → 4

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	36.9b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
▶	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 1979 to 1187 computations (40% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
✓	0.1b	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series66.0ms (0.7%)

Counts

3 → 76

Calls

3 calls:

35.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
23.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
9.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 50

Calls

3 calls:

7.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
3.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
0.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
409×	`fma-def_binary64`
381×	`*-commutative_binary64`
328×	`cancel-sign-sub-inv_binary64`
307×	`distribute-lft-out--_binary64`

Counts

126 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1977
1	294	1809
2	1038	1772
3	2450	1761
4	4893	1761
5	4986	1761

prune106.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	108	5	113

Error

0.0b

Counts

113 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	12.5b	(fma.f64 2 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) l) 3)) U)
▶	0.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	31.2b	(fma.f64 2 (.f64 l (.f64 (sqrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) (sqrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) U)
✓	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2018 to 1319 computations (34.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
✓	14.3b	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))

series2.4s (26%)

Counts

4 → 120

Calls

4 calls:

1.4s	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
877.0ms	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))
106.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
57.0ms	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`associate-*r/_binary64`
30×	`pow1_binary64`
17×	`cbrt-div_binary64`
17×	`sinh-def_binary64`
16×	`pow1/3_binary64`

Counts

4 → 100

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))))
5.0ms	(.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (*.f64 2 (sinh.f64 l)))))
3.0ms	(cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))
0.0ms	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

simplify146.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-neg_binary64`
274×	`associate-r_binary64`
269×	`associate-l_binary64`
248×	`associate--l+_binary64`
239×	`cancel-sign-sub-inv_binary64`

Counts

220 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	5712
1	772	5254
2	2323	4642
3	4851	4642
4	5268	4642

prune277.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	254	5	259

Error

0.0b

Counts

259 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	12.5b	(fma.f64 2 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) l) 3)) U)
✓	0.5b	(fma.f64 (.f64 (.f64 (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l)))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cbrt.f64 (.f64 J (.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	31.2b	(fma.f64 2 (.f64 l (.f64 (sqrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))) (sqrt.f64 (.f64 J (cos.f64 (.f64 1/2 K)))))) U)
✓	0.3b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 9046 to 5839 computations (35.5% saved)

regimes363.0ms (3.9%)

Accuracy

Total 0.0b remaining (51.2%)

Threshold costs 0.0b (51.2%)

Counts

36 → 1

Compiler

Compiled 7139 to 5269 computations (26.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample4.0s (43.1%)

Algorithm

1×

intervals

Results

921.0ms	1678×	body	1024	valid
853.0ms	1962×	body	1024	invalid
391.0ms	4387×	body	128	valid
332.0ms	1164×	body	512	valid
314.0ms	3391×	body	128	invalid
259.0ms	984×	body	512	invalid
127.0ms	712×	body	256	valid
75.0ms	459×	body	256	invalid
49.0ms	59×	body	2048	valid

Compiler

Compiled 146 to 109 computations (25.3% saved)

Details

analyze731.0ms (7.8%)

sample216.0ms (2.3%)

simplify69.0ms (0.7%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series49.0ms (0.5%)

rewrite19.0ms (0.2%)

simplify202.0ms (2.2%)

prune123.0ms (1.3%)

localize12.0ms (0.1%)

series110.0ms (1.2%)

rewrite7.0ms (0.1%)

simplify114.0ms (1.2%)

prune80.0ms (0.9%)

localize12.0ms (0.1%)

series66.0ms (0.7%)

rewrite12.0ms (0.1%)

simplify99.0ms (1.1%)

prune106.0ms (1.1%)

localize15.0ms (0.2%)

series2.4s (26%)

rewrite26.0ms (0.3%)

simplify146.0ms (1.6%)

prune277.0ms (3%)

regimes363.0ms (3.9%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.0s (43.1%)

Profiling